# Power Grid

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• Topic: Electric power transmission, Transmission line, Capacitor
• Pages : 8 (1250 words )
• Published : January 28, 2013

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EI2435
Faults and Transients on Transmission Lines

Wang Wei weiwan@kth.se 1/12/2011

1. Introduction
Project 1 is about fault currents and transients on transmission lines that may occur due a lightning strike to an overhead line. In this case the transmission line is energized from one side and it’s other side is terminated in a Gas Insulated Substation, see Fig. 1. Several issues will be investigated from this system such as transient overvoltages and short-circuit currents.

Fig.1 Transmission line model

1.1 Given parameters
System voltage Table 1. Basic power line data 420 kV 20 m 13 m 25 cm 25 mm 3800 Ohmm 0.5 m 0.5 m Do = 400 mm, Di = 120 mm

Average height above ground Phase-to-phase distance Triplex conductor, circumscribing diameter Conductor diameter Soil resistivity Tower grounded with metallic hemisphere of radius Generation station neutral grounded with metallic hemisphere of radius Co-axial GIS tube filled with SF6. Outer andd inner diameter

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2.1 Stationary LLG fault current
A phase-to-phase to ground (LLG) fault occurs in the middle of the line, i.e. YY/2 km from each sub-station. OHL parameters The theory developed by Carson give the approximate expression for the distance to return conductor as a function of the resistivity of the earth and the frequency

D  658

f

 658

3800  5736.31m 50

The geometric mean radius is given by

GMR  3 3  0.025 / 2   0.25 / 2   0.0837m
2

1 D 1 5736.31 L11  L22  L33  2 107 (  ln )  2 107 (  ln )  2.277 106 H / m 4 GMR 4 0.0837 Z11  Z22  Z33  j 2 fL11  l  j 29.69 
L12  L21  L23  L32  2 107 ln D 5736.31  2 107 ln  1.218 106 H / m d12 13

Z12  Z21  Z23  Z32  j 2 fL12  l  j15.88  L13  L31  2 107 ln D 5736.31  2 107 ln  1.08 106 H / m d13 26

Z13  Z31  j 2 fL13  l  j14.08 
The impedance matrix can be obtained

 j 29.69 Z   j15.88   j14.08 

j15.88 j 29.69 j15.88

j14.08  j15.88   j 29.69  

The capacitance for OHL

2 0 r 2 0 r   9.02 1012 F / m 2H 2  20 ln ln GMR 0.0837 C1  c1  l  9.02 1012  83000  0.5  3.74 107 F c1  GIL parameters

2

L0  2 107 ln c0 

Do  2.4  107 H / m Di

2 0 r  4.62  1011 F / m D ln o Di

C0  4.62  1011  80  3.7  109 F

2.1.1 Generators neutral are solidly grounded

Fig 2. Equivalent circuit for generators neutral are solidly grounded For solid grounded generators neutral, the current in the phase c (normal value) is much smaller than the short circuit current in phase a and b, to simply the calculation, Ic is assumed to be zero.

U ao  U a U ao  Z11 I a  Z12 I b  U bo  U b   U bo  Z 21 I a  Z 22 I b  I 0  c The short circuit current in phase a and b

I a  15.44  69.9 kA I b  15.44129.9 kA
The induced voltage in phase c

U c  U c 0  U c  U c 0  Z31I a  Z32 Ib  165.1129.6 kV

2.1.2 Generators neutral is isolated

3

Fig 3. Equivalent circuit for generators neutral is isolated

 U ao  U a  U bo  U b  0  Ic  Ib  I a  U  U  I  Z a c shunt  U c 0  0  ao Z shunt  1 1    j 4223.3  7 j (C1  C0  C ) j 2  50(3.74 10  2  3.7 109  2 109 )

The short circuit current in phase a b and c

I a  15.2  60 kA I b  15.2120 kA I c  0.0085150 kA The induced voltage in phase c

U c  U c 0  U c  U c 0  Z31I a  Z32 Ib  242.8 kV

2.2 Touch voltage
The expression of touch voltage is given by

V 

I f 2

1 1    a x

For the short circuit current in case 2.1.1,

3800 15.44 103  1 1   1 1 V     9.3 103    kV  2  0.5 x   0.5 x  Where x is the distance from feet to the tower, assume x=1, the touch voltage will reach 9300 kV.

4

2.3 Temperature increase of the power line
From the balance of the power, one can derive the relationship between the temperature rise and the current impulse in the certain time interval

W  cv m I 2 Rdt  cv md I 2...